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Journal of Lie Theory 31 (2021), No. 4, 1015--1024
Copyright Heldermann Verlag 2021

Boundedness of Hausdorff Operators on Hardy Spaces over Homogeneous Spaces of Lie Groups

Adolf R. Mirotin
Dept. of Mathematics and Programming Technologies, Francisk Skorina Gomel State University, Sovietskaya 104, Gomel 246019, Belarus

The aim of this note is to give boundedness conditions for Hausdorff operators on Hardy spaces H1 with the norm defined via (1,q) atoms over homogeneous spaces of Lie groups with doubling property and to apply the obtained results to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres.

Keywords: Hausdorff operator, Lie group, homogeneous space, Hardy space, generalized shift operator of Delsarte.

MSC: 43A85, 47G10, 22E30.

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